Unit 2 Module 2a
GEOG246-346
1 Working with raster data
We are now going to start working with the raster package. raster is a highly developed but older package than sf, so it was not written with the tidyverse or sf in mind. The upshot of this is that operations involving raster-vector interactions will often require coercion of sf to sp objects. That is not a major obstacle, however.
The material in this section assumes that the reader is familiar with standard raster GIS operations and concepts, ranging from projections and transformations to moving windows, raster algebra, terrain analysis, and the like.
We’ll use the following datasets in this section:
library(geospaar)
farmers <- system.file("extdata/farmer_spatial.csv", package = "geospaar") %>% read_csv(show_col_types = FALSE)
roads <- system.file("extdata/roads.shp", package = "geospaar") %>% st_read
districts <- system.file("extdata/districts.shp", package = "geospaar") %>%
st_read2 raster basics
2.1 Raster* classes
We’ll start off by learning about the basic raster classes, which we will do by building our own objects from scratch, starting with a RasterLayer
2.1.1 RasterLayer
# Chunk 1
# #1
e <- extent(c("xmin" = 27, "xmax" = 29, "ymin" = -16, "ymax" = -14))
#
# #2
r <- raster(x = e, res = 0.25, crs = crs(districts))
#
# #3
set.seed(1)
values(r) <- sample(1:100, size = ncell(r), replace = TRUE) # 3
# r[] <- sample(1:100, size = ncell(r), replace = TRUE)
# r <- setValues(x = r, values = sample(1:100, size = ncell(r), replace = TRUE))par(mar = c(0, 0, 0, 4))
plot(st_geometry(districts), col = "grey", reset = FALSE)
plot(r, add = TRUE)We just used several functions from the raster package to create a random raster named r that has a 1/4 degree resolution and covers an area of 2 X 2 degrees in southern Zambia. This particular raster is a temporary one that lives in memory.
Let’s walk through the labelled code. In # 1, we use raster’s extent function to define the boundaries of the raster, and then in # 2 use the raster function to create a raster from the resulting Extent object e, assigning a CRS using the “crs” argument, which in turn uses raster’s crs to extract the crs from districts (#3). crs is similar to sf::st_crs, but outputs a different class of object that can’t be used by raster. The raster function can create a raster from many different types of input objects (passed to argument “x”), per ?raster:
filename (character), Extent, Raster, SpatialPixels, SpatialGrid*, object, ‘image’, matrix, im, or missing. Supported file types are the ‘native’ raster package format and those that can be read via rgdal
Line # 2 creates an empty raster r with no cell values, so in # 3 we assign some randomly selected values into r. Note the method of assignment, using the values function; there are two other lines commented out below # 3 that show different ways of doing the same job.
The plot of r over districts uses the plot method defined for raster* objects. Note that it automatically creates a continuous legend, and also note that raster::plot can work with sf::plot.
Let’s look now at the structure of the object r.
# Chunk 2
r
#> class : RasterLayer
#> dimensions : 8, 8, 64 (nrow, ncol, ncell)
#> resolution : 0.25, 0.25 (x, y)
#> extent : 27, 29, -16, -14 (xmin, xmax, ymin, ymax)
#> crs : +proj=longlat +datum=WGS84 +no_defs
#> source : memory
#> names : layer
#> values : 1, 100 (min, max)
class(r)
#> [1] "RasterLayer"
#> attr(,"package")
#> [1] "raster"
typeof(r)
#> [1] "S4"
slotNames(r)
#> [1] "file" "data" "legend" "title" "extent" "rotated" "rotation" "ncols"
#> [9] "nrows" "crs" "history" "z"
values(r)
#> [1] 68 39 1 34 87 43 14 82 59 51 97 85 21 54 74 7 73 79 85 37 89 37 34 89
#> [25] 44 79 33 84 35 70 74 42 38 20 28 20 44 87 70 40 44 25 70 39 51 42 6 24
#> [49] 32 14 2 45 18 22 78 65 70 87 70 75 81 100 13 40
# slot(slot(r, "data"), "values") # identical to values(r)
res(r)
#> [1] 0.25 0.25r is an S4 object that has fairly different slots compared to sf objects. We are not going to go into all of them, but it is useful to know the @file, @data, @extent, and @crs slots. @file itself holds a number of slots, but you should know the @file@name slot, which contains the file name and path for grids that that are read in from disk (it is empty in the case of r, since it is held in memory). @data contains many slots also, but the main one of interest is the @data@values slot, which can be accessed with the values function directly, or less directly using slot (both approaches are shown above). Interestingly, the resolution information is not stored in any of the slots of r, but rather calculated from the @extent and @ncols and @nrows slots by the res function.
2.1.2 RasterStack and RasterBrick
We have just seen how to create a RasterLayer and learned a bit about the structure of this kind of object, which is two-dimensional. We are now going to learn about three-dimensional rasters, which come in two flavors: RasterStack and RasterBrick. Before we proceed, we first need to create some new data.
# Chunk 3
r2 <- r > 50
r3 <- r
set.seed(1)
values(r3) <- rnorm(n = ncell(r3), mean = 10, sd = 2)
l <- list(r, r2, r3)We used r to create two new rasters, r2 and r3. r2 was made by using a logical operator (>) to find the locations where r’s values exceed 50, creating a binary raster where 1 indicates the matching pixels, and 0 those that don’t. r3 was made by using r as a template, then overwriting the values with numbers generated randomly from a normal distribution (rnorm). These were then combined into list l.
# Chunk 4
s <- stack(l)
# s <- stack(r, r2, r3) # also works
names(s) <- c("r", "r2", "r3")
s
#> class : RasterStack
#> dimensions : 8, 8, 64, 3 (nrow, ncol, ncell, nlayers)
#> resolution : 0.25, 0.25 (x, y)
#> extent : 27, 29, -16, -14 (xmin, xmax, ymin, ymax)
#> crs : +proj=longlat +datum=WGS84 +no_defs
#> names : r, r2, r3
#> min values : 1.0000, 0.0000, 5.5706
#> max values : 100.00000, 1.00000, 14.80324
b <- brick(s)
b
#> class : RasterBrick
#> dimensions : 8, 8, 64, 3 (nrow, ncol, ncell, nlayers)
#> resolution : 0.25, 0.25 (x, y)
#> extent : 27, 29, -16, -14 (xmin, xmax, ymin, ymax)
#> crs : +proj=longlat +datum=WGS84 +no_defs
#> source : memory
#> names : r, r2, r3
#> min values : 1.0000, 0.0000, 5.5706
#> max values : 100.00000, 1.00000, 14.80324
plot(b, nr = 1)In the preceding code blocks, we use l to create a RasterStack and RasterBrick. These are very similar things, but have a few key differences. A RasterStack is a series of rasters that have the same extent and resolution, which are “stacked” on top of one another in the order that they are given in the input list. The stacked layers can from any number of files stored in different areas on disk. A RasterBrick does the same thing (stacks RasterLayers on top of one another), but is more restrictive because the layers, if read off disk, must be contained within a single file. This makes the RasterBrick less flexible than the RasterStack, but it has the advantage of faster processing times (according to ?brick).
Applying plot to a stack or brick results in the automatic plotting of each layer into its own sub-window, with coordinates along the plot axes. You can specify numbers of rows and columns in your plotting device using the “nc” and “nr” arguments to raster::plot.
Here’s a more informative (by putting it over a map of Zambia) way of plotting the layers in s (works for b also):
# Chunk 5
par(mfrow = c(1, 3), mar = c(0, 0, 0, 4))
for(i in 1:nlayers(s)) {
districts %>% st_geometry %>% plot(col = "grey")
plot(s[[i]], add = TRUE)
}2.2 Reading and writing rasters
So far we have used Raster* data that are held in memory. Let’s write these out onto disk and then read them back in. Write these to your notebooks/data folder (per instructions in Unit 2 module 1 vignette.
# Chunk 6
# #1 - write to disk
writeRaster(r, filename = file.path(tempdir(), "r.tif"))
writeRaster(r2, filename = file.path(tempdir(), "r2.tif"))
writeRaster(r3, filename = file.path(tempdir(), "r3.tif"))
writeRaster(b, filename = file.path(tempdir(), "b.tif"))
# #2 - read back in each individual raster and recreate stack
r <- raster(file.path(tempdir(), "r.tif"))
r2 <- raster(file.path(tempdir(), "r2.tif"))
r3 <- raster(file.path(tempdir(), "r3.tif"))
s <- stack(list(r, r2, r3)) # recreate stack
# #3 - programmatic creation of stack
fs <- dir(tempdir(), pattern = "r.*.tif", full.names = TRUE)
l <- lapply(fs, raster)
s <- stack(l)
# s <- fs %>% lapply(raster) %>% stack # pipeline approach works, too
# #4 - read in brick
b <- raster(file.path(tempdir(), "b.tif")) # incorrect, reads in just 1st layer
b <- brick(file.path(tempdir(), "b.tif")) # correct, reads in whole brickIn #1 above, we use writeRaster to write out each of the three individual rasters to a geotiff, and write b to a three-band geotiff. In #2 we use the raster function to read back in the individual rasters, and then recreate stack s from those. #3 is a more programmatic way of doing #2, using the dir function to read the directory, looking for filenames matching a pattern, and returning the full paths to the matching files. These paths are then used in an lapply to read the files in with raster, recreating list l, which is then stacked. The pipeline approach that wraps up these commands in one line is shown commented out below that.
Blocks #2 and #3 illustrate how stack can be used to create a three-dimensional grid from different files, which differ from what you see next in #4, where the “b.tif” is read back into a brick. You will see the comment there that says that the first line in #4 is incorrect, because using raster only results in the first raster being read in.
2.3 From vector to raster and back again
Now that you know the major Raster* classes, and how to read and write them to disk, let’s figure out how to change between raster and vector types.
2.3.1 Vector to raster
We have several vector datasets that come with geospaar which we can rasterize, starting with the district boundaries.
# Chunk 7
# #1
zamr <- raster(x = extent(districts), crs = crs(districts), res = 0.1)
values(zamr) <- 1:ncell(zamr)
#
# #2
districts <- districts %>% mutate(ID = 1:nrow(.))
distsr <- districts %>% rasterize(x = ., y = zamr, field = "ID") %>% print()
#> class : RasterLayer
#> dimensions : 98, 117, 11466 (nrow, ncol, ncell)
#> resolution : 0.1, 0.1 (x, y)
#> extent : 21.99978, 33.69978, -18.02621, -8.226213 (xmin, xmax, ymin, ymax)
#> crs : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0
#> source : memory
#> names : layer
#> values : 1, 72 (min, max)
par(mar = c(0, 0, 0, 4))
plot(distsr, axes = FALSE, box = FALSE)In #1, we took an initial step to define a raster (zamr) that has the properties of resolution (0.1 decimal degrees), CRS, and extent that we want our rasterized vector to have. We set the extent of this raster to that of districts, using extent to get the bounding box coordinates (extent retrieves the same parameters as sf::st_bbox, but the output is in a different format).
In #2, we use rasterize to (as the name says) rasterize districts. The “y” argument is where we feed in zamr, the raster object that is the “target” for rasterizing districts. The “field” argument supplies the column names of the values that we want rasterized. In this case, we have to first create an “ID” variable for districts, in order to give an integer for each district name, as the district names (a character variable) cannot be written to the raster. Notice that we have constructed this as a pipeline (with print as the last step, to show the raster metadata). The commented out code below it shows how it can be done with more conventional syntax.
Our plot removes the coordinate-labelled axes and box that otherwise drawn around raster plots by default.
Next we rasterize the farmers dataset, which requires a little more prep to be meaningful:
# Chunk 8
# #1
zamr2 <- raster(x = extent(districts), crs = crs(districts), res = 0.25)
values(zamr2) <- 1:ncell(zamr2)
# #2
farmersr <- farmers %>% distinct(uuid, .keep_all = TRUE) %>%
dplyr::select(x, y) %>% mutate(count = 1) %>%
st_as_sf(coords = c("x", "y"), crs = 4326) %>%
rasterize(x = ., y = zamr2, field = "count", fun = sum) %>% print()
#> class : RasterLayer
#> dimensions : 39, 47, 1833 (nrow, ncol, ncell)
#> resolution : 0.25, 0.25 (x, y)
#> extent : 21.99978, 33.74978, -17.97621, -8.226213 (xmin, xmax, ymin, ymax)
#> crs : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0
#> source : memory
#> names : layer
#> values : 1, 152 (min, max)
# #3
par(mar = c(0, 0, 1, 4))
districts %>% st_union %>%
plot(col = "grey", border = "grey",
main = expression(paste("N farmers per 0.25", degree, " cell")))
plot(farmersr, add = TRUE)In #1, we create a coarser scale (0.25 degree) version of zamr (zamr2), because we want our final raster to count how many farmers responding to our survey are found in each grid cell. The resolution of 0.1 degrees used for zamr is a bit too fine to convey the information nicely in a plot.
In #2, we do the rasterization as part of a pipeline. The first two lines prepare the farmers dataset. Recall that farmers consists of weekly reporting data sent to us by a large number of farmers, which means that we have multiple reports sent by the same farmer (and thus repeated coordinates for each farmer). So we need to reduce farmers down to just one row for each individual farmer, so that we have just a single set of coordinates for each. We do that by using distinct on the uuid variable, using .keep_all = TRUE so that we retain the coordinates, and add a new count variable (which assigns a value of 1 to each farmer) before converting farmers to sf in the third line. We then rasterize the count variable, using the sum function to aggregate the number of farmers per 0.25\(\circ\) grid cell.
The resulting plot (#3) shows that most cells have less than 20 farmers. We add an extra plot decoration step, using expression with paste to add a superscript degree symbol to our plot title.
You can also rasterize line features, much as we did for points and polygons, but rasterize is exceedingly slow for lines, so we are not doing that here. However, there is code below that shows how one could so that with the roads dataset (subset to roads greater than 100 km long):
# Chunk 9
roadsr <- roads %>% filter(as.numeric(st_length(.)) > 1000000) %>%
mutate(ID = 1:nrow(.)) %>% st_transform(crs = 4326) %>%
rasterize(., zamr, field = "ID")2.3.2 Raster to vector
raster gives us functions that allow us to transform rasters to vectors.
# Chunk 10
# #1
dists_fromr <- rasterToPolygons(x = distsr, dissolve = TRUE) %>% st_as_sf
# #2
farmers_fromr <- rasterToPoints(x = farmersr, spatial = TRUE) %>% st_as_sf
par(mar = c(0, 0, 0, 0))
dists_fromr %>% st_geometry %>% plot(col = topo.colors(n = nrow(districts)))
farmers_fromr %>% plot(pch = 20, col = "red", add = TRUE)Vectorizing rasters and vectorizing back again means that you end up with lower resolution vectors if the raster is fairly coarse. You will note that this has occurred here, both in converting the rasterized districts back to polygons (#1) and the rasterized farmer counts back to points (#2). There are several things to note here. First, we used different functions for vectorizing polygons and points. Second, we piped each vectorization output to st_as_sf, because the endresult of the rasterTo* functions is an sp object, so the extra coerces those to sf.
2.4 Projections
Up until now, our Raster* data have been in geographic coordinates systems. Let’s transform these to projected coordinates, using the rasterized districts as an example.
# Chunk 11
# #1
zamr_alb <- projectRaster(from = zamr, res = 11000, crs = crs(roads),
method = "ngb")
# #2
distsr_alb <- projectRaster(from = distsr, to = zamr_alb, method = "ngb")
par(mfrow = c(1, 2), mar = c(0, 0, 1, 4))
plot(distsr, main = "GCS rasterized districts", axes = FALSE, box = FALSE)
plot(distsr_alb, main = "Albers rasterized districts", axes = FALSE,
box = FALSE)In our first step (#1), we apply projectRaster to our zamr object, transforming it to the Albers projection used by roads (the “crs” argument). We define an output “res” of 11,000 m, or 11 km, which is reasonably close to the 1/10th of a degree resolution of zamr. We also choose a “method” for calculating the transformed values in the new raster. In this case, since zamr has values that are basically an integer index of grid cells, we use the “ngb” (nearest neighbor) option, to avoid the bilinear interpolation that would occur by default (see ?projectRaster).
The result, zamr_alb, then becomes a reference raster (i.e. the raster defining the parameters) for other rasters that need to be reprojected, which is how we use it when reprojecting distsr_alb (# 2). In this case, we pass zamr_alb to the “to” argument, and don’t need the “res” or “crs” arguments (because the function reads those values from “zamr_alb”). Here we again use the “ngb” method so that we do not change the values of the categorical identifier of each district. You can see how the interpolation choice matters in the plot below, which compares the bilinear to ngb method–see how the bilinear approach changes values along district boundaries?
# Chunk 12
distsr_alb2 <- projectRaster(from = distsr, to = zamr_alb, method = "bilinear")
par(mfrow = c(1, 2), mar = c(0, 0, 1, 4))
plot(distsr_alb2, main = "Bilinear reprojection", axes = FALSE, box = FALSE)
plot(distsr_alb, main = "Nearest neighbor", axes = FALSE, box = FALSE)A bilinear interpolation is more appropriate for a raster of continuous values, or one where it makes sense to have values averaged during the reprojection process, such as the farmersr dataset.
2.5 Practice
2.5.1 Questions
What is a primary difference between
sfands4object classes?What function should you use to read and write a multi-layer raster?
What are the difference between
stackandbrick?What class of object do
raster’s vectorization functions produce?
2.5.2 Code
Create a new raster
r4, usingr3(above) as a template. Update the values ofr4using numbers randomly selected from a uniform distribution ranging between 0 and 1. Create another rasterr5by finding the values greater than 0.5 in r4. Recreate the listlwithr,r2,r3,r4, andr5, and then create and plot stacks2.Create a new brick
b2by applying thebrickfunction tos2and writing it out to disk asb2.tif, specifying the path to yournotebooks/datafolder.Following the steps in Chunk 8, recreate
farmersrby re-rasterizingfarmersat a 0.2 degree resolution. Plot the result.Project the new 0.2 degree resolution
farmersrto an Albers projection with a target resolution of 20 km (20,000 m), calling itfarmersr_alb. Chunk 11 is your guide, but reproject using a bilinear rather than nearest neighbor interpolation (see?projectRaster). Make a two panel plot comparingfarmersron the left, plotted over the unioned districts of Zambia in grey, withfarmersr_albon the right, plotted over the unioned districts of Zambia in grey (and transformed to Albers). Code in Chunks 8 and 11 can help.Convert
distsrto ansfpolygons object, usingrasterToPolygonswithdissolve = TRUE. Plot the result without coercing tost_geometry.
3 Pre-processing and local to global statistics
This unit starts to focus on some of the analyses you can do with raster data, focusing specifically on calculating statistics from rasters. We will start in on that after doing a bit more raster processing and preparation.
3.1 Pre-processing
We will keep working with the data from the previous sections, adding in a new dataset that loads with geospaar, chirps.
# Chunk 13
data("chirps")Since we are recycling some of the objects from the previous section but you might have cleared your workspace, here is code that will allow you to quickly rebuild the datasets we will use in this next section, without having to hunt back through the previous section to find it.
zamr <- raster(x = extent(districts), crs = crs(districts), res = 0.1)
values(zamr) <- 1:ncell(zamr)
distsr <- system.file("extdata/districts.shp", package = "geospaar") %>%
st_read %>% mutate(ID = 1:nrow(.)) %>%
rasterize(x = ., y = zamr, field = "ID")
zamr2 <- raster(x = extent(districts), crs = crs(districts), res = 0.25)
farmersr <- system.file("extdata/farmer_spatial.csv", package = "geospaar") %>% read_csv() %>% distinct(uuid, .keep_all = TRUE) %>%
dplyr::select(x, y) %>% mutate(count = 1) %>%
st_as_sf(coords = c("x", "y"), crs = 4326) %>%
rasterize(x = ., y = zamr2, field = "count", fun = sum)There a few important things we missed doing in the first section. But first let’s talk about the new data we just loaded, chirps. We have a help file in geospaar describing the dataset, which provides daily rainfall values at ~5 km resolution, estimated from satellite observations (of cloud top temperature, I believe) and corrected by weather station observations. CHIRPS is a near global product that extends back to the 1970s (read more about it here), but we have just subset 28 days of data over Zambia.
# Chunk 14
chirps
#> class : RasterBrick
#> dimensions : 197, 234, 46098, 28 (nrow, ncol, ncell, nlayers)
#> resolution : 0.05, 0.05 (x, y)
#> extent : 21.95, 33.65, -18.05, -8.200001 (xmin, xmax, ymin, ymax)
#> crs : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0
#> source : memory
#> names : Y16299, Y16300, Y16301, Y16302, Y16303, Y16304, Y16305, Y16306, Y16307, Y16308, Y16309, Y16310, Y16311, Y16312, Y16313, ...
#> min values : 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
#> max values : 21.33322, 17.76521, 22.12555, 32.39063, 19.46936, 28.53870, 19.03967, 26.27214, 22.93114, 18.90109, 22.52590, 20.18479, 22.41066, 21.03057, 22.64041, ...
# names(chirps) <- paste0("Y", 16299:16326)
names(chirps)
#> [1] "Y16299" "Y16300" "Y16301" "Y16302" "Y16303" "Y16304" "Y16305" "Y16306" "Y16307" "Y16308"
#> [11] "Y16309" "Y16310" "Y16311" "Y16312" "Y16313" "Y16314" "Y16315" "Y16316" "Y16317" "Y16318"
#> [21] "Y16319" "Y16320" "Y16321" "Y16322" "Y16323" "Y16324" "Y16325" "Y16326"That tells us a bit more about the chirps subset that we have, including the names we have given to each of the layers, which correspond to the particular day in the rainfall time series, beginning with Y16299 (Y16 = 2016, 299 = julian day 299, or October 25th) and ending with Y16326 (11/22/2016). Note that chirps is actually a RasterBrick that we have saved as an .rda file that installs with geospaar for convenience.
Let’s have a look at a few of the days in chirps:
# Chunk 15
par(mfrow = c(1, 3), mar = c(0, 0, 1, 4))
for(i in 1:3) {
leg <- ifelse(i == 3, yes = TRUE, no = FALSE) # 1
plot(chirps[[i]], main = names(chirps)[[i]], axes = FALSE, box = FALSE,
zlim = c(0, max(chirps[1:3])), legend = leg) # 2
districts %>% st_union %>% plot(add = TRUE)
}The above plots the first three dates in chirps and drapes Zambia’s outline over it. These data are obviously not just confined to Zambia, so that sets up our next set of processing steps we need to do. But let’s first examine the plotting code a bit more, which shows us two new things. First, there is the use of ifelse, which we use to set up a conditional placement of a legend for iteration 3. When i == 3, we tell plot to add the legend to the figure panel being plotted by making the variable leg == TRUE (otherwise it is FALSE). leg is passed to the “legend” argument of plot. We did this because we wanted just one legend that reflects the range set by the “zlim” argument within plot. “zlim” sets a limit on the range of data values that are plotted, which in this case falls between 0 and the maximum rainfall value observed across all three of the plotted dates (max(chirps[1:3])). That gives all three plots a common scale, so, given that, why clutter up the plots with three legends showing the same thing?
The second thing: we haven’t discussed this yet, but you will see in the example above that indexing into a RasterStackBrick to select a particular layer or layers is achieved through [[]]. This applies to both single ([[x]]) and multiple/recursive ([[x:y]]) indexing, which differs from indexing into a list, where you use [x:y] for multiple selection. Selection by layer names also works (chirps[[c("Y16299", "Y16300")]]; chirps[["Y16299"]])
3.1.1 Masking
We are interested in the rainfall data within Zambia’s borders, so we need to mask out the values of chirps that fall outside of Zambia:
# Chunk 16
test_m <- mask(x = chirps[[1]], mask = districts)
par(mar = c(0, 0, 0, 4))
plot(test_m, axes = FALSE, box = FALSE) In the code above, we use the districts data to mask out the portions of chirps (the first day in the time series only) falling outside of Zambia. Let’s apply that to the entire chirps dataset:
# Chunk 17
chirpsz <- mask(x = chirps, mask = districts)
set.seed(1)
ind <- sample(1:nlayers(chirpsz), size = 3)
plot(chirpsz[[ind]], axes = FALSE, box = FALSE, nr = 1)The new chirpsz dataset contains all rainfall days with the values outside of Zambia converted to NA. The three plots are randomly selected from the layers of chirpsz, as a check to confirm that the masking was applied to all layers.
3.1.2 Cropping
If we need to chop a raster down to a smaller region, we can crop it. crop uses the extent of another object to achieve this.
# Chunk 18
chirps1_dist72 <- crop(x = chirpsz[[1]], y = districts %>% slice(72))
par(mar = c(0, 0, 0, 2))
chirps1_dist72 %>% plot(axes = FALSE, box = FALSE)
districts %>% st_geometry %>% plot(add = TRUE)
districts %>% st_centroid %>% st_coordinates %>%
text(x = ., labels = row.names(.))The above uses the extent of district 72 (dist72) to crop the first layer of chirpsz. Note that in the plotting step we can pipe the cropped raster to plot, and also that we can label the district numbers on the plot by extracting their centroid coordinates and passing these into the “x” argument of text, and then using the row.names of the piped-in data.frame of centroid coordinates as the labels.
Cropping is important if we want to confine further analyses to a particular sub-region. However, if we just want to focus our plot to a particular region, then we can simply zoom the plot to that region (without cropping) using an extent object.
# Chunk 19
par(mar = c(0, 0, 0, 2))
plot(chirpsz[[1]], axes = FALSE, box = FALSE, ext = extent(districts[72, ]))
districts %>% st_geometry %>% plot(add = TRUE)
districts %>% st_centroid %>% st_coordinates %>%
text(x = ., labels = row.names(.))3.1.2.1 A function-writing detour
As we write this, we find ourselves growing weary of repeatedly writing “axes = FALSE, box = FALSE” into the plot function, even with RStudio’s handy tab completion. This repeated use of the exact same code is the sort of situation that calls for writing your own function.
# Chunk 20
plot_noaxes <- function(x, axes = FALSE, box = FALSE, mar = c(0, 0, 1, 4),
...) {
if(!class(x) %in% c("RasterLayer", "RasterStack", "RasterBrick", "Extent")) {
stop("This function is intended for rasters only", call. = FALSE)
}
par(mar = mar)
plot(x, axes = axes, box = axes, ...)
}The function above (not run in the block above, because it is written into geospaar) takes care of the axes and box problem by setting their default arguments to FALSE. It also sets the default plot margins to the ones we have mostly been using so far (leaving room on the right for the legend and at the top for a title), and it checks whether the object being passed to it belongs to one of the raster classes (failing if it doesn’t). Otherwise, it retains all of the other functionality of raster::plot, and has the “…” argument, meaning you can pass other eligible arguments to it.
Let’s see how it works:
# Chunk 21
plot_noaxes(chirpsz[[1]])
# chirpsz[[1]] %>% plot_noaxes # also works in a pipelineThat will make plotting easier moving forward.
3.1.3 Aggregating/disaggregating
To change to resolution of a raster object, you can use aggregate to make a coarser resolution, or disaggregate to decrease the resolution. To make chirpsz match the 0.1 resolution of distsr (the rasterized districts), we do this:
# Chunk 21
chirpsz1agg <- aggregate(x = chirpsz[[1]], fact = 2, fun = mean)
chirpsz1agg
#> class : RasterLayer
#> dimensions : 99, 117, 11583 (nrow, ncol, ncell)
#> resolution : 0.1, 0.1 (x, y)
#> extent : 21.95, 33.65, -18.1, -8.200001 (xmin, xmax, ymin, ymax)
#> crs : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0
#> source : memory
#> names : Y16299
#> values : 0, 12.18843 (min, max)We aggregate the first layer of chirpsz by a factor of 2 (fact = 2), taking the average of the aggregated pixels (fun = mean). Since the starting resolution was 0.05, doubling the pixel size takes it to 0.1. We could have chosen to aggregate all layers, and we could have chosen a different aggregation function (e.g. sum, max).
To disaggregate, there are two options:
# Chunk 22
chirpsz1km <- disaggregate(x = chirpsz[[1]], fact = 5)
# chirpsz1km <- disaggregate(x = chirpsz[[1]], fact = 5, method = "bilinear")
chirpsz1km
#> class : RasterLayer
#> dimensions : 985, 1170, 1152450 (nrow, ncol, ncell)
#> resolution : 0.01, 0.01 (x, y)
#> extent : 21.95, 33.65, -18.05, -8.200001 (xmin, xmax, ymin, ymax)
#> crs : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0
#> source : memory
#> names : Y16299
#> values : 0, 18.00534 (min, max)The first option is the default one, which just breaks apart each pixel into the number of smaller new pixels specified by the factor, assigning each new pixel the same value as its larger parent. Here we specified a factor of 5, leading to an output resolution of 0.01 (~1 km), and thus 25 times the number of pixels as in the original chirpsz[[1]] (run ncell(chirpsz1km) / ncell(chirpsz[[1]]) to see).
The second way (commented out), is to set method = bilinear, which interpolates during disaggregation. In this case, disaggregate does the job using the resample function, which we will see next.
3.1.4 Resampling
Resampling is done for many reasons, but one particularly common case is as a final step following aggregation or disaggregation, when it is needed to co-register the resulting grid to another grid.
# Chunk 23
chirps125 <- aggregate(x = chirpsz[[1]], fact = 5) # no fun b/c default is mean
s <- stack(chirps125, farmersr) # fails
par(mar = c(1, 1, 1, 1))
plot(extent(chirps125), axes = FALSE, col = "blue")
plot(extent(farmersr), add = TRUE, col = "red")After aggregating chirpsz layer 1, we try and fail to stack the result with farmersr, because (as the plot of extents show, and the warning tells) the two objects have different extents. So, another approach is needed:
# Chunk 24
farmersr_rs <- resample(x = farmersr, y = chirps125)
s <- stack(chirps125, farmersr_rs)
names(s) <- c("rain", "farmer_count")
plot_noaxes(s)We resample farmersr to chirps125rs, since chirps125rs has the larger extent. However, there is one more thing we should do before using these data, and that is an adjustment to farmersr. Have a look at this:
plot_noaxes(s$farmer_count >= 0)
plot(st_geometry(st_union(districts)), add = TRUE)This shows that there are no places where there are 0 farmers–because the original data contributing to farmersr (the second layer in s) was derived from point locations representing the approximate locations of where farmers were interviewed. The data thus have no points where there were 0 farmers interviewed (it would be silly to conduct an interview with no subject), thus everywhere outside of interview locations is assigned a no data value. These are not analyzed in raster operations. So we have to fix this if we want to have the full area of Zambia in the second layer of our stack.
s$farmer_count[is.na(s$farmer_count)] <- 0
s$farmer_count <- mask(s$farmer_count, s$rain)
plot_noaxes(s$farmer_count)
plot(st_geometry(st_union(districts)), add = TRUE) Now all the areas in
s$farmer_counts where no interviews were conducted area set to 0.
We can then stack and perform subsequent analyses that draw on both layers, e.g. finding areas where rainfall exceeded 1 mm and where there was more than 1 farmer:
# Chunk 25
plot_noaxes(s$farmer_count > 1 & s$rain > 1)
# (s$rain > 1 & s$farmer_count > 1) %>% plot_noaxes # also works3.2 Analyses
Let’s move on now to some analyses with raster data.
3.2.1 Global statistics
The most basic analyses to perform on rasters is to calculate global summary statistics, i.e. statistics calculated across all cell values:
# Chunk 26
cellStats(x = chirpsz[[1]], stat = "mean") # for a single date
cellStats(x = chirpsz[[c(5, 7, 14)]], stat = "mean")
summary(chirpsz[[1:3]])
#> Y16299 Y16300 Y16301
#> Min. 0.00000 0.00000 0.000000
#> 1st Qu. 0.00000 0.00000 0.000000
#> Median 0.00000 0.00000 0.000000
#> 3rd Qu. 0.00000 0.00000 0.000000
#> Max. 18.00534 17.76521 8.853778
#> NA's 20995.00000 20995.00000 20995.000000cellStats lets you calculate specific statistics from the cell values of a lone RasterLayer, or for a single, multiple, or all layers in a RasterStackBrick. summary (a generic) returns the quintile values and counts the number of NA or no data cells. Both functions by default remove NA values (which are in many if not most rasters), which is something that usually has to be specified when trying to apply these statistical functions to an ordinary vector, e.g.
# Chunk 27
v <- values(chirpsz[[1]])
mean(v)
#> [1] NA
mean(v, na.rm = TRUE)
#> [1] 0.6971701v is a vector of all of the values from the first layer in the rainfall brick, including its NA values. mean returns an NA if you don’t tell the function to remove NA values first. This is important to remember, because both spatial and non-spatial data often have missing values, so you will have to deal with them explicitly in many cases.
Here’s a more programmatic way of using cellStats:
# Chunk 28
# #1
rain_stats <- lapply(list(mean, sum, sd, cv), function(x) {
cellStats(x = chirpsz, stat = x)
})
names(rain_stats) <- c("mean", "sum", "sd", "cv")
# #2
rain_statsf <- do.call(cbind, rain_stats) %>% data.frame %>%
mutate(date = as.Date(gsub("Y", "", row.names(.)), "%y%j"))
# do.call(cbind, rain_stats) %>% data.frame
# do.call(cbind, rain_stats) %>% row.names %>% gsub("Y", "", .)
# do.call(cbind, rain_stats) %>% row.names %>% gsub("Y", "", .) %>%
# as.Date(., "%y%j")
# #3
ps <- lapply(c("mean", "sum", "sd", "cv"), function(x) { # x <- "mean"
ggplot(rain_statsf %>% dplyr::select(date, all_of(x))) +
geom_line(aes_string("date", x)) + xlab("")
})
cowplot::plot_grid(plotlist = ps)In #1 we use lapply to calculate 4 different statistics over all dates in chirpsz, meaning that we get a time series for each statistic as calculated over all of Zambia.
In #2, we use a pipeline to bind the summary time series vectors into a data.frame (one statistic per column), and then do some gymnastics to convert the row names of the data.frame, which are constructed from the layer names of chirpsz (which are stored as “Y16XXX”, where XXX is the julian day) to a vector of dates. Work through the commented out code below this line, which breaks down the steps used to create the date variable. gsub first replaces the “Y” in each name, and then as.Date parses the remaining numbers into an actual date. The “%y%j” construction tells as.Date which parts of the character string relate to which part of a date: %y = two digit year; %j = julian day; placed next to one another %y%j means these two elements are immediately adjacent to one another in the string.
We use lapply to set up four ggplot objects in #3 (note the use of aes_string rather than aes, which allows the variable names to be passed as string, rather than unquoted), and then use cowplot::plot_grid to put those plots in a grid, using the “plotlist” argument to receive the input list of ggplots.
The results in the plot above are actually quite interesting. The top two panels show when the rainy season gets underway in earnest (just after Nov 8). The bottom two panels show two measures of variability, the standard deviation (SD) and coefficient of variation (CV, i.e. SD / mean). These two measures summarize the spatial variability of rainfall falling across Zambia on each day–SD increases as the amount of rain increases (which is expected–SD is usually positively correlated with the mean), whereas CV declines as rainfall increases, indicating that a progressively larger area of the country receives rainfall as the month progresses, so there is less spatial variability. There is a big spike in CV on November 8, which corresponds to a drop in mean and total rainfall. However, that drop masks the fact that there are a few small patches that received a decent amount of rainfall, thus leading to a high CV (see next plot below).
# Chunk 29
plot_noaxes(chirpsz[[15]], main = paste("CV =", round(rain_stats$cv[15])))Another way to summarize raster data is visually, using a histogram (raster has a generic hist function)
# Chunk 30
par(mfrow = c(1, 3))
hist(chirpsz[[15:17]], col = "blue", xlab = "mm")This variant plots a histogram per layer in the Raster* object (but we told it to plot 1 row, 3 columns, instead of the default (2 rows, 2 columns)).
freq is another way to summarize raster values that is similar to hist but without the automatic plot.
# Chunk 31
f <- freq(chirpsz[[1]]) %>% print()
#> value count
#> [1,] 0 21053
#> [2,] 1 234
#> [3,] 2 698
#> [4,] 3 817
#> [5,] 4 660
#> [6,] 5 544
#> [7,] 6 432
#> [8,] 7 306
#> [9,] 8 175
#> [10,] 9 59
#> [11,] 10 42
#> [12,] 11 41
#> [13,] 12 27
#> [14,] 13 7
#> [15,] 14 3
#> [16,] 15 2
#> [17,] 16 2
#> [18,] 18 1
#> [19,] NA 20995Here we apply freq to a dataset with continuous values, although this function is probably best reserved for categorical rasters. However, it produces reasonable results here.
3.2.2 Local statistics
The previous section showed us how to produce statistics calculated across the entire raster. Now we will learn to calculate local, or neighborhood, statistics.
3.2.2.1 Zonal
One way local statistics can be calculated is by defining zones and then calculating statistics within those zones.
# Chunk 32
# #1
# zonemu <- zonal(x = chirpsz, z = distsr, fun = "mean") # fails b/c extent
# #2
distsr_rs <- resample(x = distsr, y = chirpsz, method = "ngb") # match extent
zonemu <- zonal(x = chirpsz, z = distsr_rs, fun = "mean")
head(zonemu)[, 1:5]
#> zone Y16299 Y16300 Y16301 Y16302
#> [1,] 1 0.00000000 0.0000000 0.0000000 1.8976312
#> [2,] 2 0.01322501 0.0000000 0.0000000 0.0000000
#> [3,] 3 6.04584049 1.8021238 0.0000000 4.4494707
#> [4,] 4 0.00000000 0.3011147 0.0201552 0.0000000
#> [5,] 5 6.25742351 3.6532615 1.0868976 0.4739815
#> [6,] 6 0.00000000 0.0000000 0.0000000 0.0000000That creates a matrix (truncated here to show the first 6 rows and 5 columns) of mean rainfall within each zone ( district), by date. The first attempt to run zonal (#1) would have failed because of mismatched extents (and therefore was commented out so it wouldn’t run), so we used resample in #2 to align extents before re-running zonal.
To map zonal statistics back onto their zones, we need to use another function, subs.
# Chunk 33
distr_rfmu <- zonemu %>% data.frame %>% dplyr::select(1:2) %>%
subs(x = distsr_rs, y = ., by = "zone")
plot_noaxes(distr_rfmu)subs replaces the values in a raster by other values contained within a data.frame (we converted zonemu from matrix and selected the first two columns, with column containing the zone number) that correspond to a variable that has the same values as those in the raster (in this case the district IDs). subs can be slow-ish on big rasters.
3.2.2.2 Focal
Another way of calculating image statistics is to use a moving window/neighborhood approach. This is done with the focal function, which can be used to calculate a large number of different statistics. Here’s we’ll just show you the mean (also known as a low pass filter), with a few permutations to illustrate the concept. Disclaimer: This section assumes that you have applied moving window functions/low pass/high pass filters in your GIS/remote sensing classes so far, and thus are familiar with the calculations. If not, please be sure to ask about this in class.
# Chunk 34
# #1
wmat <- matrix(1 / 9, nrow = 3, ncol = 3)
chirps1_focmu1 <- focal(x = chirpsz[[1]], w = wmat)
# #2
wmat <- matrix(1, nrow = 3, ncol = 3)
chirps1_focmu2 <- focal(x = chirpsz[[1]], w = wmat, fun = mean)
# #3
wmat <- matrix(1, nrow = 5, ncol = 5)
chirps1_focmu3 <- focal(x = chirpsz[[1]], w = wmat, fun = mean)
# #4
wmat <- matrix(1, nrow = 5, ncol = 5)
chirps1_focmu4 <- focal(x = chirpsz[[1]], w = wmat, fun = mean, na.rm = TRUE)
# #5
wmat <- matrix(1 / 9, nrow = 5, ncol = 5)
chirps1_focmu5 <- focal(x = chirpsz[[1]], w = wmat, na.rm = TRUE)
# plots
l <- list(chirps1_focmu1, chirps1_focmu3, chirps1_focmu4, chirps1_focmu5)
titles <- c("3X3 NAs not removed", "5X5 NAs not removed",
"5X5 NAs removed properly", "5X5 NAs removed improperly")
par(mfrow = c(2, 2))
for(i in 1:length(l)) {
plot_noaxes(l[[i]], main = titles[i])
}We have 5 variants above. In #1, we calculate the focal mean the recommended way, which is to:
- Define a matrix (
wmat) that contains the weights thatfocalapplies to each pixel when making neighborhood calculations. In this case, the matrix is 3X3, which is the size of our moving window, and the weights are distributed equally across all pixels and sum to 1 (each gets a weight of 1/9) focalthen passes over each image pixel, and multiplies those weights by each pixel value in the neighborhood, and then sums those to get the mean- It sums the values because
sumis the default value of the argument “fun” in the functionfocal, which is why we have not even specified the argument “fun” in Block 1
Note that the way focal is coded here does not remove NA pixels, thus any neighborhood having even a single NA pixel is itself turned into NA, i.e. all 9 pixels in the neighborhood. Thus the entire boundary of Zambia is trimmed down accordingly (by 2 pixels). This result is illustrated in the upper left panel of the plot above.
The code in #2 is a slower way of doing the same thing. It passes the mean function to focal’s “fun” argument. The weights matrix in this case has 1s throughout; since we are not using the default “fun=sum” in focal and mean is doing the work, we can’t modify (by weighting) the pixel values if we want the correct mean. We also do not remove NA values from the calculation, so the results are identical (and thus not plotted).
In #3, we use the same approach as in #2, but expand the neighborhood to 5X5. You will see in the upper right plot that Zambia shrank even more (by 4 pixels).
In #4, we again pass mean to focal, and have a 5X5 neighborhood, but here we specify na.rm = TRUE, which means that focal passes TRUE to the “na.rm” argument of mean. This results in NAs being removed from each neighborhood before calculating the mean, thus boundary pixels are not lost (note the larger area in the lower left plot above). This is the correct way to remove NAs when calculating focal means.
The improper way of removing NAs from focal calculations is shown in #5, this time using the faster approach demonstrated in Block 1. The lower right plot shows how pixels near Zambia’s border have artificially low values. This result is because the approach relies on a weighted mean, and because NAs are removed, the weights do not sum to 1 and thus the mean is underestimated.
3.2.3 Analyzing the Z dimension
If we have a RasterStackBrick, we have three dimensions (x, y, z). Often we want to analyze the values in the Z dimension (which may represent time, spectral bands, or unrelated spatial predictors in a model) without altering the x and y dimensions.
The workhorse for doing this sort of analysis is calc, which allows you to apply pretty much any function to the Z-dimension of a RasterStackBrick.
# Chunk 35
# #1
rain_zmu <- calc(x = chirpsz, fun = mean)
rain_zsd <- calc(x = chirpsz, fun = sd)
rain_zrng <- calc(x = chirpsz, fun = range)
# #2
rain_zstack <- stack(rain_zmu, rain_zsd, rain_zrng)
names(rain_zstack) <- c("Mean", "StDev", "Min", "Max")
plot_noaxes(rain_zstack)In #1 we pass mean, sd, and range to “fun” in calc. Note that range always returns two values, so calc conveniently returns a two-layer brick that contains the minimum in the first layer and the maximum in the second.
In #2 we then stack the three outputs, and rename the layers something meaningful so that plot_noaxes can plot them all at once.
You will see from the resulting plot that “Min” has only one value, 0, which makes sense for a rainfall time series (every pixel is likely to have at least one day of no rainfall over the course of a month).
3.3 Practice
3.3.1 Questions
How do
cellStats,focal, andzonaldiffer from one another?How do you
disaggregatea raster with interpolation?How do you run
calcon images with different resolutions or extents?
3.3.2 Code
Run
as.Date("10-11-2017", "%m-%d-%Y"),as.Date("10-11-17", "%m-%d-%y"),as.Date("101117", "%m%d%y"), andas.Date("10112017", "%m%d%Y")to get a better sense of date vectors work. Also try outlubridate::mdy("10-11-2017")andlubridate::as_date("20171011").Convert
farmersto a 0.1 degree raster (farmersr2) that contains the count of farmers per grid cell. Usedistsras the target raster so that the extents align.Use
zonalonfarmersr2to calculate the total number of farmers per district (usedistsrto provide the zones), and then map them back onto the districts/zones usingsubs. Plot the result.Use
focalto calculate forchirpsz[[20]]the i) standard deviation within a 3X3 and 5X5 window, and ii) the maximum value in each 3X3 and 5X5 neighborhood. Do not remove NAs. Combine the results in astack, as above, and then plot them usingplot_noaxes.Crop
chirpsz[[1]]using the extent ofdistricts[57, ], and disaggregate it to 0.01 resolution using both the default and bilinear methods. Plot the results side by side usingplot_noaxes.Use
calcwithchirpszto calculate the total rainfall in the time series, the coefficient of variation, and the median. Stack the results and plot with meaningful titles usingplot_noaxes(hint: name the layers of thestack), outputting plots on 1 row with 3 columns.